The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2...

Racetovb4j

Racetovb4j

Answered

2022-02-03

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-3, how do you find a possible formula for P(x)?

Answer & Explanation

bubble53zjr

bubble53zjr

Expert

2022-02-04Added 14 answers

Since each root is a linear factor, we can write:
P(x)=x2(x1)2(x+3) 
=x2(x22x+1)(x+3) 
=x5+x45x3+3x2 
Any polynomial that contains these zeros and at least these multiplicities is going to be a multiple (scalar or polynomial) of this P(x) 
Answer: 
P(x)=x5+x45x3+3x2

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